DOI: 10.1007/jhep08(2026)115 ISSN: 1029-8479
On anomaly-free 4d $$ \mathcal{N} $$ = 4 and 6d (2,0) conformal supergravities and UV finiteness of Poincaré supergravities
R. Kallosh, A. A. Tseytlin
A
bstract
We review the structure of superconformal anomalies in 4d
$$ \mathcal{N} $$
N
= 4 conformal supergravity (CSG) coupled to a number N
v
of
$$ \mathcal{N} $$
N
= 4 vector multiplets and 6d (2,0) CSG coupled to N
T
of (2,0) tensor multiplets. Anomalies cancel if N
v
= 4 and N
T
= 26 respectively. If the CSG part of the action is dropped and N
v
= 6 + n
v
, the first theory is classically equivalent to the 4d
$$ \mathcal{N} $$
N
= 4 Poincaré supergravity (PSG) coupled to n
v
vector multiplets, while the second one with N
T
= 5 + n
T
is classically equivalent to the 6d (2,0) PSG coupled to n
T
tensor multiplets. We suggest that these facts imply that divergences in the 4d PSG with n
v
vectors should be proportional to n
v
+ 2 and similarly in the 6d PSG with n
T
tensors to n
T
– 21. This conjecture appears to be consistent with most of the known results of explicit scattering amplitude computations in these 4d and 6d PSG theories, apart from one coefficient in the 3-loop mixed vector scattering amplitude computed in arXiv:1305.4876.